Details

Time bar (total: 1.5m)

sample158.0ms

Algorithm
intervals
Results
102.0ms85×body10240exit
29.0ms270×body80valid
6.0ms5×body1280valid
4.0ms6×body640valid
3.0ms8×body320valid
1.0ms5×body160valid

simplify23.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
23.0ms
(- (log (+ 1 (exp x))) (* x y))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize20.0ms

Local error

Found 2 expressions with local error:

0.5b
(log1p (exp x))
0.0b
(- (log1p (exp x)) (* y x))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
5×add-log-exp
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
3×expm1-log1p-u fma-neg prod-diff
2×pow1 log1p-udef add-cbrt-cube diff-log add-exp-log insert-posit16 log1p-expm1-u
1×sub-neg flip3-- log1p-expm1 flip--
Counts
2 → 34
Calls
2 calls:
Slowest
10.0ms
(- (log1p (exp x)) (* y x))
1.0ms
(log1p (exp x))

series145.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
87.0ms
(log1p (exp x))
58.0ms
(- (log1p (exp x)) (* y x))

simplify679.0ms

Counts
17 → 40
Calls
17 calls:
Slowest
125.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
92.0ms
(fma (* (cbrt (log1p (exp x))) (cbrt (log1p (exp x)))) (cbrt (log1p (exp x))) (- (* x y)))
82.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
70.0ms
(/ (exp (log1p (exp x))) (exp (* y x)))
57.0ms
(/ (+ 1 (exp x)) (exp (* y x)))

prune360.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize72.0ms

Local error

Found 4 expressions with local error:

14.4b
(/ (- (pow (log1p (exp x)) 3) (pow (* y x) 3)) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))
0.7b
(* (log1p (exp x)) (log1p (exp x)))
0.7b
(pow (log1p (exp x)) 3)
0.5b
(log1p (exp x))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
71×add-sqr-sqrt
39×times-frac
37×*-un-lft-identity
32×difference-of-squares
29×add-cube-cbrt
25×sqr-pow
13×associate-/l*
12×pow1
11×unpow-prod-down cube-prod
9×add-cbrt-cube add-exp-log
5×expm1-log1p-u
4×difference-cubes insert-posit16 log1p-expm1-u distribute-lft-out-- add-log-exp
3×pow-unpow associate-/r* swap-sqr associate-*r* associate-*l*
2×associate-/r/ associate-/l/
1×pow2 cube-mult pow-to-exp cbrt-undiv log1p-udef clear-num pow-pow frac-2neg flip3-+ pow-plus flip3-- unpow3 div-sub div-exp pow-prod-down pow-exp prod-exp log1p-expm1 pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ div-inv flip-- rem-cube-cbrt unswap-sqr
Counts
4 → 141
Calls
4 calls:
Slowest
131.0ms
(/ (- (pow (log1p (exp x)) 3) (pow (* y x) 3)) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))
5.0ms
(* (log1p (exp x)) (log1p (exp x)))
2.0ms
(pow (log1p (exp x)) 3)
0.0ms
(log1p (exp x))

series480.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
218.0ms
(/ (- (pow (log1p (exp x)) 3) (pow (* y x) 3)) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))
105.0ms
(pow (log1p (exp x)) 3)
102.0ms
(* (log1p (exp x)) (log1p (exp x)))
54.0ms
(log1p (exp x))

simplify28.0s

Counts
144 → 153
Calls
144 calls:
Slowest
709.0ms
(/ (* (* (- (pow (log1p (exp x)) 3) (pow (* y x) 3)) (- (pow (log1p (exp x)) 3) (pow (* y x) 3))) (- (pow (log1p (exp x)) 3) (pow (* y x) 3))) (* (* (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))))
627.0ms
(/ (+ (pow (log1p (exp x)) (/ 3 2)) (sqrt (pow (* y x) 3))) (sqrt (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))))
491.0ms
(pow (* (cbrt (log1p (exp x))) (cbrt (log1p (exp x)))) 3)
485.0ms
(+ (* (* (log1p (exp x)) (log1p (exp x))) (* (log1p (exp x)) (log1p (exp x)))) (- (* (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (* (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))))
434.0ms
(pow (* (cbrt (log1p (exp x))) (cbrt (log1p (exp x)))) 3)

prune2.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize50.0ms

Local error

Found 4 expressions with local error:

14.5b
(/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (- (pow (log1p (exp x)) 3) (pow (* y x) 3)))
0.7b
(* (log1p (exp x)) (log1p (exp x)))
0.7b
(pow (log1p (exp x)) 3)
0.5b
(log1p (exp x))

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
71×add-sqr-sqrt
39×times-frac
37×*-un-lft-identity
32×difference-of-squares
29×add-cube-cbrt
25×sqr-pow
13×associate-/r*
12×pow1
11×unpow-prod-down cube-prod
9×add-cbrt-cube add-exp-log
5×expm1-log1p-u
4×difference-cubes insert-posit16 log1p-expm1-u distribute-lft-out-- add-log-exp
3×pow-unpow swap-sqr associate-*r* associate-*l* associate-/l*
2×associate-/r/ associate-/l/
1×pow2 cube-mult pow-to-exp cbrt-undiv log1p-udef clear-num pow-pow frac-2neg flip3-+ pow-plus flip3-- unpow3 div-exp pow-prod-down pow-exp prod-exp log1p-expm1 pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ div-inv flip-- rem-cube-cbrt unswap-sqr
Counts
4 → 140
Calls
4 calls:
Slowest
201.0ms
(/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (- (pow (log1p (exp x)) 3) (pow (* y x) 3)))
10.0ms
(* (log1p (exp x)) (log1p (exp x)))
3.0ms
(pow (log1p (exp x)) 3)
1.0ms
(log1p (exp x))

series617.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
321.0ms
(/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (- (pow (log1p (exp x)) 3) (pow (* y x) 3)))
131.0ms
(pow (log1p (exp x)) 3)
112.0ms
(* (log1p (exp x)) (log1p (exp x)))
52.0ms
(log1p (exp x))

simplify27.2s

Counts
144 → 152
Calls
144 calls:
Slowest
684.0ms
(/ 1 (sqrt (- (pow (log1p (exp x)) 3) (pow (* y x) 3))))
658.0ms
(/ (* (* (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))) (* (* (- (pow (log1p (exp x)) 3) (pow (* y x) 3)) (- (pow (log1p (exp x)) 3) (pow (* y x) 3))) (- (pow (log1p (exp x)) 3) (pow (* y x) 3))))
475.0ms
(+ (* 3/4 (* (log 2) (pow x 2))) (+ (* 3/8 (* (pow (log 2) 2) (pow x 2))) (+ (pow (log 2) 3) (* 3/2 (* (pow (log 2) 2) x)))))
447.0ms
(pow (* (cbrt (log1p (exp x))) (cbrt (log1p (exp x)))) 3)
421.0ms
(- (pow (log1p (exp x)) (/ 3 2)) (sqrt (pow (* y x) 3)))

prune2.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

localize58.0ms

Local error

Found 4 expressions with local error:

9.1b
(/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (- (log1p (exp x)) (* y x)))
8.8b
(* (/ 1 (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))) (/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (- (log1p (exp x)) (* y x))))
0.7b
(* (log1p (exp x)) (log1p (exp x)))
0.7b
(* (log1p (exp x)) (log1p (exp x)))

rewrite674.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
36×*-un-lft-identity
34×times-frac add-cube-cbrt
32×add-exp-log
22×add-cbrt-cube
21×associate-*r* associate-*l*
20×pow1
10×prod-exp
9×div-exp
8×unswap-sqr
6×swap-sqr associate-/r/ cbrt-unprod
5×cbrt-undiv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* pow-prod-down *-commutative div-inv associate-/l*
2×pow2 rec-exp flip3-+ pow-plus flip3-- 1-exp pow-sqr pow-prod-up flip-+ flip-- associate-/l/
1×frac-times clear-num frac-2neg associate-*l/ associate-*r/
Counts
4 → 153
Calls
4 calls:
Slowest
414.0ms
(* (/ 1 (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))) (/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (- (log1p (exp x)) (* y x))))
247.0ms
(/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (- (log1p (exp x)) (* y x)))
6.0ms
(* (log1p (exp x)) (log1p (exp x)))
5.0ms
(* (log1p (exp x)) (log1p (exp x)))

series552.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
237.0ms
(/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (- (log1p (exp x)) (* y x)))
147.0ms
(* (/ 1 (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))) (/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (- (log1p (exp x)) (* y x))))
92.0ms
(* (log1p (exp x)) (log1p (exp x)))
76.0ms
(* (log1p (exp x)) (log1p (exp x)))

simplify18.7s

Counts
140 → 165
Calls
140 calls:
Slowest
939.0ms
(* (* (* (/ 1 (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))) (/ 1 (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))) (/ 1 (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))) (/ (* (* (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))) (* (* (- (log1p (exp x)) (* y x)) (- (log1p (exp x)) (* y x))) (- (log1p (exp x)) (* y x)))))
770.0ms
(* (/ (* (* 1 1) 1) (* (* (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))) (/ (* (* (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))) (* (* (- (log1p (exp x)) (* y x)) (- (log1p (exp x)) (* y x))) (- (log1p (exp x)) (* y x)))))
656.0ms
(* (/ (* (* 1 1) 1) (* (* (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))) (* (* (/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (- (log1p (exp x)) (* y x))) (/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (- (log1p (exp x)) (* y x)))) (/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (- (log1p (exp x)) (* y x)))))
499.0ms
(/ (* (* (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))) (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x))))) (* (* (- (log1p (exp x)) (* y x)) (- (log1p (exp x)) (* y x))) (- (log1p (exp x)) (* y x))))
488.0ms
(+ (- (log 1) (log (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))))) (log (/ (+ (* (log1p (exp x)) (log1p (exp x))) (+ (* (* y x) (* y x)) (* (log1p (exp x)) (* y x)))) (- (log1p (exp x)) (* y x)))))

prune1.5s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.3b

regimes62.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch2.0ms

end0.0ms

sample3.8s

Algorithm
intervals
Results
2.5s2514×body10240exit
755.0ms8413×body80valid
119.0ms250×body640valid
102.0ms126×body1280valid
88.0ms204×body320valid
27.0ms126×body160valid